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Principles of Data Analytics
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Terms in this set (39)
Let's say I gave three different types of food to people taking tests, and there are 9 samples of test scores. How can you tell if food makes a difference in test scores?
One-Way ANOVA
Compare safety of three types of cars. Determine if sample mean for each type is equal for each type. Use a = 0.05.
One-Way ANOVA
We want to study the effect of drug treatment on 18 individuals. Based on two ages and three treatment types, each person gets a score. Can you tell if the drug makes a difference on scores? Can you tell if age makes a difference on scores?
Randomized Block Design (Block independence)
Two-Way ANOVA (Interaction effects between blocks)
Report says that 49% of teachers in US are in union. Is this true for a specific state? Take a random sample of teachers in state to see what percentage are in union.
Z-test (proportions)
Report says 90% of homes in CA have internet access. Researchers want to test if this percentage is higher. They take a random sample of 1000 homes in CA and find 920 have access.
Z-test (proportions)
Company claims that out of its 40 employees, 10% receve an "exceeds expectations" rating. Girl wonder if the % is lower, so she takes random sample of 10 employees ratings.
Z-test (Proportions)
Report says 26% of Americans speak more than one language. Is this higher for a specific city? It was found that 40 out of 120 people spoke more than one language.
Z-test (proportions)
Person wants to test if greater than 50% of adults support a tax increase.
Z-test (proportions)
Manufacturer claims thickness is 7.5. Worker wants to check if this is true. He takes a random sample of 10 and obtains average thicknesses of 7.57. If the manufacturer's claim of s is 0.1, is this true?
Z-test (mean)
Say a person wants to determine if a drug has an effect. Two groups of test subjects are made, one receiving the drug and the other receiving a placebo. The sample size, standard deviation, and mean for the first are 900, 4.05, and 9.78, respectively. The sample size, standard deviation, and mean for the second are 1000, 4.28, and 15.10, respectively. Does the drug have an effect?
Z-test (for two means)
Man takes some bottles from a plant and measures their liquid volume. He find the sample average and standard deviation to be 503 and 5, respectively. The mean volume is supposed to be 500. Is the mean amount from the sample different from what it's supposed to be?
T-test
Man suspects that more than 100 messages are sent per day to his chat group. He takes a random sample over 7 days and finds data is strongly skewed to the right with a sample mean of 125 and standard deviation of 44. Are the number of messages sent per day actually more than 100?
T-test
A report says teachers in a district have 5 years of experience on average. A man wants to test if this is actually higher than reality. He samples 25 teachers, and found the sample mean is 4 and standard deviation 2.
T-test
A study says the mean is 18, and a person wants to test to see if this is actually too high. He tests 7 samples.
T-test
A study claims that the mean is 0, but someone wants to test if this is not true. He tests 6 samples.
T-test
A teacher wants to know if her students are good at basic math. She samples 6 students, and they get scores 62, 92, 75, 68, 83, and 95. Can the teacher have a 90% confidence that the mean score is greater than 70?
T-test
Doctors test to see if adding fiber results in higher scores. They make a more test group and a test group with high fiber. Assume the samples come from the same population (i.e. the population distributions are the same).
T-test (pooled)
Say you go to a restaurant and as for a distribution on their customers per day. Should you accept or reject the restaurant owner's data for how many customers he expects?
X2-test (goodness-of-fit)
Students want to know if multiple choice answers A, B, C, and D on tests are skewed toward one letter. Teachers claim that they're not. Is it true?
X2-test (goodness-of-fit)
In a game, a man expects to either win, tie, or lose with equal frequency. Is this true? He took a random sample of 24 games and recorded their outcomes.
X2-test (goodness-of-fit)
Girl wants to test the claim that the s of firemen is < 25 lbs. She selects a random sample of 20 firemen and finds their standard deviation is 23.2.
X2-test (variance)
Say you have a pool of homogeneous students divide into two groups A and B. Groups A and B listen to different kinds of music before taking a test. Do the two music types give different performance variances? The sample scores for each group are given.
F-test (for variance)
Say you want to test a drug on the same individuals, and you get a scores on those individuals before and after use. The scores are listed below. Did the drug have an effect?
Paired t-test
What are the assumptions behind Binomial Distributions? How do you test for these?
· Trials are independent à replacement or sample size <10% pop.
· Each trial has 2 discrete outcomes
· Fixed # of trials
The probability of success for each trial is constant.
What are the assumptions behind Poisson Distributions? How do you test for these?
·One time interval isn't different than any other.
Independence. One sample doesn't affect another.
What are the assumptions behind the Paired T-test (for related samples)? How do you test for these?
· Random
· Normality
o N > 30
o Parent population normal?
o Bell-shape w/ no outliers
No independence (since they're related samples)
What are the assumptions behind the X2-test for variations? How do you test for these?
· Random
· Independence
o Replacement
o Sample size <10% pop.
· Normality
VERY important à parent population must be normal on this
What are the assumptions behind the X2-test for goodness-of-fit? How do you test for these?
· Random
· Large counts à expected number of each category must be >= 5
· Independence
o Replacement
o Sample size <10% pop.
· Normality
VERY important à parent population must be normal on this
What are the assumptions behind the T-test for means with two sample groups? How do you test for these?
· Random
· Independence
o Replacement
o Sample size <10% pop.
· Normality
o N > 30
o Parent population normal?
o Bell-shape w/ no outliers
· Independence between groups
· Equal variation between groups?
o Yes: pooled t-test
No: Welch's t-test
What are the assumptions behind the T-test for means? How do you test for these?
· Random
· Independence
o Replacement
o Sample size <10% pop.
· Normality
o N > 30
o Parent population normal?
Bell-shape w/ no outliers
What are the assumptions behind the Z-test for means with two sample groups? How do you test for these?
· Random
· Independence
o Replacement
o Sample size <10% pop.
· Normality
o Expected # success: np̂ > 10
Expected # failures: n(1-p̂) > 10
What are the assumptions behind the Z-test for means? How do you test for these?
· Random
· Independence
o Replacement
o Sample size <10% pop.
Normality
What are the assumptions behind one-way ANOVA? How do you test for these?
· Random
· Independence
o Replacement
o Sample size <10% pop.
· Normality (F-test is robust though)
Homogeneity of variance
What are the assumptions behind Randomized Block Design? How do you test for these?
· Random
· Independence
o Replacement
o Sample size <10% pop.
· Normality (F-test is robust though)
· Homogeneity of variance
No interaction effects between classes and blocks
What are the assumptions behind two-way ANOVA? How do you test for these?
· Random
· Independence
o Replacement
o Sample size <10% pop.
· Normality (F-test is robust though)
Homogeneity of variance
What are the assumptions behind the F-test for variations? How do you test for these?
· Random
· Independence
o Replacement
o Sample size <10% pop.
· Normality (F-test is robust though)
Homogeneity of variance
Define Central Limit Theorem, and what is its underlying assumption?
If you have a population distribution with a defined mean and variance and say you take 3 sample groups from the population, with each sample group having n samples. If you take the mean of each of the sample groups, and you plot the frequency of the sample means on a histogram, it will ALWAYS tend toward a normal distribution.
Assumption: your sample groups are coming from population(s) with the same distribution.
Define Confidence Interval
It is the range (or interval) of values that is a percentage likelihood to contain the mean.
Define Normal Distribution
Normal curve, a bell-shaped distribution of individual differences in a normal population in which most scores cluster around the average score
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